The discretetime generalized algebraic Riccati equation: Order reduction and solutions’ structure
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In this paper we discuss how to decompose the constrained generalized discretetime algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+Δ of each solution X: The first part is trivial, in the sense that it is an explicit expression of the addend X0 which is common to all solutions, so that it does not depend on the particular X. The second part can be – depending on the structure of the considered generalized Riccati equation – either a reducedorder discretetime regular algebraic Riccati equation whose associated closedloop matrix is nonsingular, or a symmetric Stein equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures.
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This research was partially supported by the Australian Research Council (grant no. FT120100604)
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